Métriques Kählériennes extrémales sur les surfaces toriques [d'après S. Donaldson]
Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1018, 21 p.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez le site de la revue.
@incollection{AST_2011__339__181_0,
     author = {Biquard, Olivier},
     title = {M\'etriques K\"ahl\'eriennes extr\'emales sur les surfaces toriques [d'apr\`es S. Donaldson]},
     booktitle = {S\'eminaire Bourbaki, volume 2009/2010, expos\'es 1012-1026},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:1018},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {339},
     year = {2011},
     zbl = {1377.53090},
     mrnumber = {2906354},
     language = {fr},
     url = {archive.numdam.org/item/AST_2011__339__181_0/}
}
Biquard, Olivier. Métriques Kählériennes extrémales sur les surfaces toriques [d'après S. Donaldson], dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1018, 21 p. http://archive.numdam.org/item/AST_2011__339__181_0/

[1] M. Abreu - Kähler geometry of toric varieties and extremal metrics, Internat. J. Math. 9 (1998), p. 641-651. | Article | MR 1644291 | Zbl 0932.53043

[2] V. Apostolov, D. M. J. Calderbank, P. Gauduchon & C. W. Tønnesen-Friedman - Hamiltonian 2-forms in Kähler geometry. III. Extremal metrics and stability, Invent. Math. 173 (2008), p. 547-601. | Article | MR 2425136 | Zbl 1145.53055

[3] C. Arezzo & F. Pacard - Blowing up and desingularizing constant scalar curvature Kähler manifolds, Acta Math. 196 (2006), p. 179-228. | Article | MR 2275832 | Zbl 1123.53036

[4] O. Biquard - Métriques kählériennes à courbure scalaire constante : unicité, stabilité, Séminaire Bourbaki, vol. 2004/2005, exp. n° 938, Astérisque 307 (2006), p. 1-31. | EuDML 252160 | Numdam | MR 2296414 | Zbl 1142.32010

[5] E. Calabi - Extremal Kähler metrics, in Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, 1982, p. 259-290. | MR 645743 | Zbl 0487.53057

[6] E. Calabi, Extremal Kähler metrics. II, in Differential geometry and complex analysis, Springer, 1985, p. 95-114. | Article | MR 780039 | Zbl 0574.58006

[7] X. Chen - The space of Kähler metrics, J. Differential Geom. 56 (2000), p. 189-234. | Article | MR 1863016 | Zbl 1041.58003

[8] X. Chen & G. Tian - Geometry of Kähler metrics and foliations by holomorphic discs, Publ. Math. Inst. Hautes Études Sci. 107 (2008), p. 1-107. | Article | EuDML 274359 | Numdam | MR 2434691 | Zbl 1182.32009

[9] T. Delzant - Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988), p. 315-339. | Article | EuDML 87558 | Numdam | MR 984900 | Zbl 0676.58029

[10] S. K. Donaldson - Remarks on gauge theory, complex geometry and 4-manifold topology, in Fields Medallists' lectures, World Sci. Ser. 20th Century Math., vol. 5, World Sci. Publ., River Edge, NJ, 1997, p. 384-403. | Article | MR 1622931

[11] S. K. Donaldson, Symmetric spaces, Kähler geometry and Hamiltonian dynamics, in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2, vol. 196, Amer. Math. Soc., 1999, p. 13-33. | MR 1736211 | Zbl 0972.53025

[12] S. K. Donaldson, Scalar Curvature and Projective Embeddings. I, J. Differential Geom. 59 (2001), p. 479-522. | Article | MR 1916953 | Zbl 1052.32017

[13] S. K. Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002), p. 289-349. | Article | MR 1988506 | Zbl 1074.53059

[14] S. K. Donaldson, Interior estimates for solutions of Abreu's equation, Collect. Math. 56 (2005), p. 103-142. | EuDML 41824 | MR 2154300 | Zbl 1085.53063

[15] S. K. Donaldson, Extremal metrics on toric surfaces : a continuity method, J. Differential Geom. 79 (2008), p. 389-432. | Article | MR 2433928 | Zbl 1151.53030

[16] S. K. Donaldson, Kähler geometry on toric manifolds, and some other manifolds with large symmetry, in Handbook of geometric analysis. No. 1, Adv. Lect. Math. (ALM), vol. 7, Int. Press, Somerville, MA, 2008, p. 29-75. | MR 2483362 | Zbl 1161.53066

[17] S. K. Donaldson, Constant scalar curvature metrics on toric surfaces, Geom. Funct. Anal. 19 (2009), p. 83-136. | Article | MR 2507220 | Zbl 1177.53067

[18] D. Guan - On modified Mabuchi functional and Mabuchi moduli space of Kähler metrics on toric bundles, Math. Res. Lett. 6 (1999), p. 547-555. | Article | MR 1739213 | Zbl 0968.53050

[19] V. Guillemin - Kaehler structures on toric varieties, J. Differential Geom. 40 (1994), p. 285-309. | Article | MR 1293656 | Zbl 0813.53042

[20] V. Guillemin, Moment maps and combinatorial invariants of Hamiltonian T n -spaces, Progress in Math., vol. 122, Birkhäuser, 1994. | MR 1301331 | Zbl 0828.58001

[21] T. Mabuchi - Uniqueness of extremal Kähler metrics for an integral Kähler class, Internat. J. Math. 15 (2004), p. 531-546. | Article | MR 2078878 | Zbl 1058.32017

[22] T. Mabuchi, An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds. I, Invent. Math. 159 (2005), p. 225-243. | Article | MR 2116275 | Zbl 1118.53047

[23] T. Mabuchi, K-stability of constant scalar curvature polarization, prepublication arXiv :0812.4093.

[24] T. Mabuchi, A stronger concept of K-stability, prepublication arXiv :0910.4617.

[25] J. Stoppa - K-stability of constant scalar curvature Kähler manifolds, Adv. Math. 221 (2009), p. 1397-1408. | Article | MR 2518643 | Zbl 1181.53060

[26] G. Székelyhidi - Optimal test-configurations for toric varieties, J. Differential Geom. 80 (2008), p. 501-523. | Article | MR 2472481 | Zbl 1167.53063

[27] G. Tian - Kähler-Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997), p. 1-37. | Article | MR 1471884 | Zbl 0892.53027

[28] N. S. Trudinger & X.-J. Wang - The affine Plateau problem, J. Amer. Math. Soc. 18 (2005), p. 253-289. | Article | MR 2137978 | Zbl 1229.53049

[29] X.-J. Wang & X. Zhu - Kähler-Ricci solitons on toric manifolds with positive first Chern class, Adv. Math. 188 (2004), p. 87-103. | Article | MR 2084775 | Zbl 1086.53067

[30] B. Zhou & X. Zhu - K-stability on toric manifolds, Proc. Amer. Math. Soc. 136 (2008), p. 3301-3307. | Article | MR 2407096 | Zbl 1155.53040